Weakly compact linear operators on space of Dunford integral function

Abstract

This study discussed the integral of Dunford and compact linear operator on space of Dunford integral function. For each f which is Dunford integral on [a,b] is defined as an operator DL by DL (x *) = x * f, for each x * ∈ X * This study resulted that the operator DL is both a continuous linear operator and weakly compact operators. Then, it was defined as the adjoint of the operator D L * by D L * ( h ) ( x * ) = ∫ a b h D L ( x * ) each h ∈ (L 1)* The adjoint operator D L * is continuous and weakly compact linear operators.

Beberapa Sifat Fungsi-Fungsi Terintegralkan Henstock-Kurzweil di Ruang Berdimensi-n

“…Penelitian mengenai integral Henstock-Kurzweil telah dilakukan oleh beberapa peneliti diantaranya mengkaji tentang integral improper dari Riemann dan hubungannya dengan integral Henstock di ℝ 𝑛 (Muldowney & Skvortsov, 2005), linearitas integral Henstock-Pettis pada Ruang Euclid ℝ 𝑛 (Rahman, 2010), karakterisasi integral Henstock-Kurzweil di ruang Euclid (Yeong, 2011), integral Henstock-Kurzweil pada [a,b] (Afiyah, 2011), Teorema Kekonvergenan Seragam Integral Henstock-Kurzweil Fungsi Bernilai 𝐶[𝑎, 𝑏] ( Ubaidillah et al, 2014), integral Henstock-Bochner dan integral Henstock-Dunford pada interval tertutup dan terbatas (Solikhin et al, 2017), dan beberapa sifat integral Henstock-Sekuensial (Malahayati, 2017). Pada artikel ini, dibahas mengenai sifat-sifat yang dipenuhi oleh fungsi-fungsi terintegralkan Henstock-Kurzweil pada ℝ 𝑛 dan beberapa sifat yang gagal dipenuhi oleh integral Henstock-Kurzweil di ruang berdimensi-n.…”